When working with fractions, many of my students seem confident in performing the different operations, but a few are still unsure of how to reduce fractions.
Although I have stressed learning the Divisibility Rules for 2, 5, 10, and the digital root for 3, 6, 9, some still have difficulty since they do not know their multiplication tables. As a mathematics tool, I have the students make Pattern Sticks, a visual and kinesthetic aid, similar to a multiplication chart like the one on the left. Notice that an extra column (blue) has been added to the chart. (In this space, a hole is punched so that a 1" ring can be inserted to store all of the sticks in one place.)